On Morita Equivalence of Partially Ordered Monoids

We show that there is one-to-one correspondence between certain algebraically and categorically defined subobjects, congruences and admissible preorders of S -posets. Using preservation properties of Pos-equivalence functors between Pos-categories we deduce that if S and T are Morita equivalent part...

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Bibliographic Details
Published in:Applied categorical structures 2014-02, Vol.22 (1), p.137-146
Main Author: Laan, Valdis
Format: Article
Language:English
Subjects:
Convex and Discrete Geometry
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
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Summary:We show that there is one-to-one correspondence between certain algebraically and categorically defined subobjects, congruences and admissible preorders of S -posets. Using preservation properties of Pos-equivalence functors between Pos-categories we deduce that if S and T are Morita equivalent partially ordered monoids and F :Pos S →Pos T is a Pos-equivalence functor then an S -poset A S and the T -poset F ( A S ) have isomorphic lattices of (regular, downwards closed) subobjects, congruences and admissible preorders. We also prove that if A S has some flatness property then F ( A S ) has the same property.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-013-9305-z